证明：因f(cosx)=cos17x.令x=(π/2)-t.===>cosx=cos[(π/2)-t]=sint.cos17x=cos[(17π/2)-17t]=cos[8π+(π/2)-17t]=cos[(π/2)-17t]=sin17t.故f(cosx)=f[cos(π/2-t)]=cos[(17π/2)-17t].===>f(sint)=sin17t.即f(sinx)=sin17x.